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This paper investigates the uplink energy efficiency (EE) of a wireless-powered cell-free massive multiple-input multiple-output (mMIMO) system with hardware impairments, considering Rician fading and maximum ratio processing, anchored in linear minimum mean-squared error (LMMSE) channel estimation. The transceivers of access points (APs) and user equipments (UEs) are non-ideal with hardware impairments. The closed-form expressions of the total uplink (UL) EE and the average harvested energy (HE) are derived by employing a non-linear energy harvesting model and coherent transmission schemes. An optimization problem is formulated to maximize the total uplink EE, in which power control coefficients for APs and UEs, and the large-scale fading decoding vectors are considered. An alternating algorithm based on successive convex approximation (SCA) is proposed to tackle the complexity issue of the non-convex optimization problem. The numerical results show that the proposed algorithm can significantly enhance the total uplink EE comparing with the equal power allocation strategies. Moreover, it is revealed that the hardware impairments on the UEs can be the primary limitation to the total uplink EE in comparison with those on the APs, however, the impact can be effectively mitigated by the proposed algorithm.
Chen et al. (Mon,) studied this question.